YES 0.808
H-Termination proof of /home/matraf/haskell/eval_FullyBlown_Fast/empty.hs
H-Termination of the given Haskell-Program with start terms could successfully be proven:
↳ HASKELL
↳ LR
mainModule Main
| ((exponent :: Float -> Int) :: Float -> Int) |
module Main where
Lambda Reductions:
The following Lambda expression
\(m,_)→m
is transformed to
The following Lambda expression
\(_,n)→n
is transformed to
↳ HASKELL
↳ LR
↳ HASKELL
↳ IFR
mainModule Main
| ((exponent :: Float -> Int) :: Float -> Int) |
module Main where
If Reductions:
The following If expression
if m == 0 then 0 else n + floatDigits x
is transformed to
exponent0 | x True | = 0 |
exponent0 | x False | = n + floatDigits x |
↳ HASKELL
↳ LR
↳ HASKELL
↳ IFR
↳ HASKELL
↳ BR
mainModule Main
| ((exponent :: Float -> Int) :: Float -> Int) |
module Main where
Replaced joker patterns by fresh variables and removed binding patterns.
↳ HASKELL
↳ LR
↳ HASKELL
↳ IFR
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
mainModule Main
| ((exponent :: Float -> Int) :: Float -> Int) |
module Main where
Cond Reductions:
The following Function with conditions
is transformed to
undefined0 | True | = undefined |
undefined1 | | = undefined0 False |
↳ HASKELL
↳ LR
↳ HASKELL
↳ IFR
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
↳ HASKELL
↳ LetRed
mainModule Main
| ((exponent :: Float -> Int) :: Float -> Int) |
module Main where
Let/Where Reductions:
The bindings of the following Let/Where expression
exponent0 x (m == 0) |
where |
exponent0 | x True | = 0 |
exponent0 | x False | = n + floatDigits x |
|
| |
| |
| |
| |
| |
are unpacked to the following functions on top level
exponentExponent0 | ww x True | = 0 |
exponentExponent0 | ww x False | = exponentN ww + floatDigits x |
exponentM | ww | = exponentM0 ww (exponentVu10 ww) |
exponentVu10 | ww | = decodeFloat ww |
exponentN | ww | = exponentN0 ww (exponentVu10 ww) |
↳ HASKELL
↳ LR
↳ HASKELL
↳ IFR
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
↳ HASKELL
↳ LetRed
↳ HASKELL
↳ NumRed
mainModule Main
| ((exponent :: Float -> Int) :: Float -> Int) |
module Main where
Num Reduction: All numbers are transformed to thier corresponding representation with Pos, Neg, Succ and Zero.
↳ HASKELL
↳ LR
↳ HASKELL
↳ IFR
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
↳ HASKELL
↳ LetRed
↳ HASKELL
↳ NumRed
↳ HASKELL
↳ Narrow
mainModule Main
| (exponent :: Float -> Int) |
module Main where
Haskell To QDPs
↳ HASKELL
↳ LR
↳ HASKELL
↳ IFR
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
↳ HASKELL
↳ LetRed
↳ HASKELL
↳ NumRed
↳ HASKELL
↳ Narrow
↳ AND
↳ QDP
↳ QDPSizeChangeProof
↳ QDP
Q DP problem:
The TRS P consists of the following rules:
new_primMinusNat(Succ(wx110), Succ(wx1000)) → new_primMinusNat(wx110, wx1000)
R is empty.
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
By using the subterm criterion [20] together with the size-change analysis [32] we have proven that there are no infinite chains for this DP problem. From the DPs we obtained the following set of size-change graphs:
- new_primMinusNat(Succ(wx110), Succ(wx1000)) → new_primMinusNat(wx110, wx1000)
The graph contains the following edges 1 > 1, 2 > 2
↳ HASKELL
↳ LR
↳ HASKELL
↳ IFR
↳ HASKELL
↳ BR
↳ HASKELL
↳ COR
↳ HASKELL
↳ LetRed
↳ HASKELL
↳ NumRed
↳ HASKELL
↳ Narrow
↳ AND
↳ QDP
↳ QDP
↳ QDPSizeChangeProof
Q DP problem:
The TRS P consists of the following rules:
new_primPlusNat(Succ(wx700), Succ(wx80)) → new_primPlusNat(wx700, wx80)
R is empty.
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
By using the subterm criterion [20] together with the size-change analysis [32] we have proven that there are no infinite chains for this DP problem. From the DPs we obtained the following set of size-change graphs:
- new_primPlusNat(Succ(wx700), Succ(wx80)) → new_primPlusNat(wx700, wx80)
The graph contains the following edges 1 > 1, 2 > 2